Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.util.Scanner;


public class test  {

public static void main(String[] args){
	Scanner sc=new Scanner(System.in);
	double n=sc.nextDouble();
	double h=sc.nextDouble();
	double b1=1;
	double b2=0;
	double h0=h;
	double a=h0/2;
	double arr[]=new double[(int)(n-1)];
	int j=(int)n-2;
	for(double i=n;i>1;i--){
		double x1=i*b1;
		double y1=-(i*h0*b1+2*a*i);
		double z1=2*a*h0;
		double h1=calculate(x1,y1,z1);
		//System.out.println(h1);
		b2=(2*a*(i-1))/(i*(h0-h1));
	arr[j]=h0-h1;
	h0=h0-h1;
	b1=b2;
	j--;
	a=(b1*h0)/2;
	
	}
	for(int i=0;i<n-1;i++){
		System.out.println(Math.abs(arr[i]));
	}
}
public static double calculate(double a,double b,double c){
	double d1=0;
	double d2=0;
	if((b*b)-(4*a*c)>0){
		
	
	 d1=(-b+Math.sqrt((b*b)-(4*a*c)))/(2*a);
	 d2=(-b-Math.sqrt((b*b)-(4*a*c)))/(2*a);
	if(d1>0) return d1;
	else return d2;}
	 return -1;
	
}
}